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Name the vertices of the chain in the clockwise direction, as A,B,C,D,E,F,G in that order.(starting from the initial point A of the ray L1 and ending with the initial point G of L2)Join CE. Through C draw a line parallel to L2 (or L1) cutting AB at H and DE at I; Through E draw a line parallel to the L1 cutting AB at J and FG at K.Consider the triangle CDI. Angle CDI= y (given). Using the property that in a triangle, the external angle at any vertex is the sum of internal angles at the other two vertices,it can be easily seen that angle DCI = x, angle CID = z.Follows x + y +z = 180 degrees.